Sequence proof

Mathman87

Can anyone give an $$\displaystyle \epsilon$$ - N proof that the sequence:

xn = $$\displaystyle {\frac {2\,{n}^{2}+3}{4\,{n}^{2}+1}}$$

tends to 1/2?

Also more generally, give the $$\displaystyle \epsilon$$ - N proof that the sequence {xn} n=1... infinity tends to x

Plato

MHF Helper
If $$\displaystyle 0 < \varepsilon < 1$$ let $$\displaystyle n > \frac{{\sqrt {\frac{5}{{2\varepsilon }} - 1} }}{2}$$.

Mathman87

Ok, i worked it through and i can understand that answer.

Im having trouble with the general proof however?